The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218214 Number of primes up to 10^n representable as sums of consecutive squares. 1
1, 5, 18, 48, 117, 304, 823, 2224, 6113, 16974, 48614, 139349 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
There are no common representations of two, three or six squares for n < 13, so
a(n) = A218208(n) + A218210(n) + A218212(n); n < 13.
LINKS
FORMULA
a(n) = sum(A218213(k),k=1..n)
EXAMPLE
a(1) = 1 because only one prime less than 10 can be represented as a sum of consecutive squares, namely 5 = 1^2 + 2^2.
a(2) = 5 because there are five primes less than 100 representable as a sum of consecutive squares: the aforementioned 5, as well as 13 = 2^2 + 3^2, 29 = 2^2 + 3^2 + 4^2, 41 = 4^2 + 5^2 and 61 = 5^2 + 6^2.
MATHEMATICA
nn = 8; nMax = 10^nn; t = Table[0, {nn}]; Do[k = n; s = 0; While[s = s + k^2; s <= nMax, If[PrimeQ[s], t[[Ceiling[Log[10, s]]]]++]; k++], {n, Sqrt[nMax]}]; Accumulate[t] (* T. D. Noe, Oct 23 2012 *)
CROSSREFS
Sequence in context: A217866 A256539 A109363 * A146213 A344311 A176145
KEYWORD
nonn,base
AUTHOR
Martin Renner, Oct 23 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 19:00 EDT 2024. Contains 372720 sequences. (Running on oeis4.)